论文标题
近bps婴儿天空
Near-BPS baby Skyrmions
论文作者
论文摘要
我们考虑了接近所谓的受限婴儿 - 凯尔姆模型的制度中的婴儿 - 凯尔姆模型，该模型是具有区域保护差异不变性的BPS模型。扰动采用小系数$ε$的标准动力学dirichlet项的形式。该模型的经典解决方案（以$ε$为领导订单）称为限制谐波图。在模型的BPS限制（$ε\至0 $）中，潜在的是标准的预端术语，带有单位拓扑电荷的解决方案是紧凑型。使用分析和数值参数，我们为大于一个的拓扑部门提供了解决问题的解决方案。我们以$ε$开发了一种扰动方案，可以通过该方案计算为BPS质量的校正。领先顺序（$ \ MATHCAL {O}（ε^1）$）的校正表明，带有拓扑费的婴儿天空均具有精力充沛的优选。绑定能量要求我们以$ε$进行三阶，以捕获扰动理论中的相关术语，但是，结合能量在$ε^2 $下的总能量有助于总能量。我们发现，在近BPS策略中，婴儿的天空是拓扑充电二的紧凑粒子，它们在一个点上彼此接触，并在吸引人的通道中以方向为方向。
We consider the baby-Skyrme model in the regime close to the so-called restricted baby-Skyrme model, which is a BPS model with area-preserving diffeomorphism invariance. The perturbation takes the form of the standard kinetic Dirichlet term with a small coefficient $ε$. Classical solutions of this model, to leading order in $ε$, are called restricted harmonic maps. In the BPS limit ($ε\to 0$) of the model with the potential being the standard pion-mass term, the solution with unit topological charge is a compacton. Using analytical and numerical arguments we obtain solutions to the problem for topological sectors greater than one. We develop a perturbative scheme in $ε$ with which we can calculate the corrections to the BPS mass. The leading order ($\mathcal{O}(ε^1)$) corrections show that the baby Skyrmion with topological charge two is energetically preferred. The binding energy requires us to go to the third order in $ε$ to capture the relevant terms in perturbation theory, however, the binding energy contributes to the total energy at order $ε^2$. We find that the baby Skyrmions - in the near-BPS regime - are compactons of topological charge two, that touch each other on their periphery at a single point and with orientations in the attractive channel.
